A160092 Decimal expansion of (617139 + 371510*sqrt(2))/569^2.

3, 5, 2, 8, 9, 4, 1, 0, 4, 1, 5, 6, 2, 2, 2, 8, 1, 2, 9, 9, 4, 8, 6, 8, 2, 4, 4, 7, 6, 4, 2, 3, 8, 1, 0, 5, 6, 3, 0, 2, 0, 8, 3, 3, 2, 2, 0, 2, 2, 3, 8, 6, 8, 1, 8, 2, 5, 7, 5, 0, 5, 6, 5, 8, 3, 7, 4, 3, 4, 7, 1, 9, 7, 6, 9, 6, 6, 2, 6, 1, 7, 1, 7, 8, 5, 0, 7, 4, 4, 0, 0, 1, 8, 4, 2, 7, 8, 2, 8, 1, 4, 6, 9, 3, 0

Offset: 1

Author

Klaus Brockhaus, May 04 2009

Keywords

• cons
• nonn

Comments

Equals Lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A101152.

Equals Lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160090.

Examples

			(617139+371510*sqrt(2))/569^2 = 3.52894104156222812994...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A101152, A160090, A002193 (decimal expansion of sqrt(2)), A160091 (decimal expansion of (587+102*sqrt(2))/569).

Programs

Magma

(617139 +371510*Sqrt(2))/569^2; // G. C. Greubel, Apr 21 2018

Mathematica

RealDigits[(617139 +371510*Sqrt[2])/569^2, 10, 100][[1]] (* G. C. Greubel, Apr 21 2018 *)

PARI

(617139 +371510*sqrt(2))/569^2 \\ G. C. Greubel, Apr 21 2018

Formula

Equals (1940 + 766*sqrt(2))/(1940 - 766*sqrt(2)).

Equals (3 + 2*sqrt(2))*(34 - 3*sqrt(2))^2/(34 + 3*sqrt(2))^2.